Sparkle is one of the many firms in the market for...

Sparkle is one of the many firms in the market for toothpaste, which is in long-run equilibrium. a. Draw a diagram showing Sparkle's demand curve, marginal-revenue curve, average-total-cost curve, and marginal-cost curve. Label Sparkle's profit-maximizing output and price. b. What is Sparkle's profit? Explain. c. On your diagram, show the consumer surplus derived from the purchase of Sparkle toothpaste. Also show the deadweight loss relative to the efficient level of output. d. If the government forced Sparkle to produce the efficient level of output, what would happen to the firm? What would happen to Sparkle's customers?

Sparkle is one of the many firms in the market for toothpaste, which is in long-run equilibrium.
a. Draw a diagram showing Sparkle's demand curve, marginal-revenue curve, average-total-cost curve, and marginal-cost curve. Label Sparkle's profit-maximizing output and price.
b. What is Sparkle's profit? Explain.
c. On your diagram, show the consumer surplus derived from the purchase of Sparkle toothpaste. Also show the deadweight loss relative to the efficient level of output.
d. If the government forced Sparkle to produce the efficient level of output, what would happen to the firm? What would happen to Sparkle's customers?

Key Concepts

Long-Run Equilibrium in Perfect Competition

In long-run equilibrium under perfect competition, firms produce at an output level where price equals both marginal cost and the minimum of average total cost. At this point, firms earn normal profit, meaning there is no incentive for new firms to enter or for existing firms to exit. The equilibrium ensures allocative and productive efficiency in the market.

Profit Maximization

Profit maximization is achieved by producing the quantity of output where marginal revenue equals marginal cost. For a competitive firm, the marginal revenue is equal to the market price, and the firm thereby determines its profit-maximizing output by equating price with marginal cost. This condition ensures that the firm does not produce too little or too much relative to the optimal level.

Cost Curves

Cost curves, including the average total cost (ATC) and marginal cost (MC) curves, are essential in analyzing a firm’s production decisions. The ATC curve reflects the per-unit cost of production, while the MC curve shows the cost added by producing one additional unit of output. Their interaction is crucial for determining the minimum average cost and the profit-maximizing output level.

Firm's Demand Curve in Perfect Competition

In a perfectly competitive market, each firm faces a horizontal (perfectly elastic) demand curve at the prevailing market price. This represents that the firm is a price taker, meaning it can sell any quantity at the market price but cannot influence the price through its individual level of output.

Consumer Surplus

Consumer surplus is the difference between what consumers are willing to pay and what they actually pay in the market. It is graphically represented as the area under the demand curve but above the market price. This concept measures the economic benefit to consumers and is a key indicator of consumer welfare.

Deadweight Loss

Deadweight loss refers to the loss of economic efficiency when the equilibrium outcome is not achieved, often due to market distortions such as taxes, subsidies, or mandate policies. It represents the loss of total surplus that occurs when a market outcome is not allocatively efficient, leading to opportunities where mutually beneficial trades between buyers and sellers fail to occur.

Government Intervention and Efficiency

Government intervention, when it forces firms to produce at a level that is considered ‘efficient’ from a broader societal perspective rather than a firm’s profit-maximizing level, can lead to unintended consequences. For the firm, such mandates might involve producing at a lower or higher quantity than optimal, potentially resulting in losses. Meanwhile, consumers might benefit through lower prices or increased supply, yet the overall market might experience distortions that lead to reduced incentives for innovation and overall inefficiencies.

Transcript

00:01 So if you look in the text, figure four shows us exactly what we're looking for.

00:07 In part a, we have a monopolistically competitive firm.

00:12 There's the demand, marginal revenue, marginal cost, and average total cost curves.

00:18 So everything there is what we need.

00:21 All we need to do is just reproduce that diagram exactly as it is.

00:25 So this is going to show the market for sparkles toothpaste.

00:32 Okay.

00:33 The first thing we need to find here is the profit maximizing output and price.

00:39 Well, we know firms always want to produce where marginal revenue equals marginal cost.

00:43 So that's here.

00:45 Quantity produced.

00:48 Normally, marginal revenue equals demand, but for the monopolistically competitive firm, that's not the case.

00:53 Instead, demand is greater than marginal revenue.

00:58 So instead of the price being marginal cost here, instead the prices here at p.

01:06 The difference between those two being the markup.

01:10 Okay.

01:10 Now, what is sparkle's profit? sparkle's profit is going to be that markup times the quantity produced.

01:23 In other words, their profit is equal to the markup.

01:26 Up on each unit times all of the units that are sold.

01:33 Now, we need to show the consumer surplus that we actually get from purchasing sparkle toothpaste.

01:41 Okay, so let's zoom in real quick, just to make this a little clearer.

01:46 Consumer surplus is always bounded at the bottom by price and bounded on the right by the demand curve.

01:57 We'll just extend the demand curve all the way to the vertical...

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